Common Core Math · High School
Distinguish between situations that can be modeled with linear functions and with exponential functions, recognizing that linear functions grow by equal differences over equal intervals and exponential functions grow by equal factors over equal intervals.
Why water teaches this standard well
Students distinguish a flat-rate water bill, which grows by the same dollar amount every month, from an algae bloom in a warm reservoir, which can grow by the same multiplying factor every week. Telling these two growth patterns apart is essential before choosing which kind of model to build.
Materials tagged with this code are written to the full standard , and each carries a written note explaining the alignment. See how we review materials.
Grade 11 Lesson plan
A 50-minute grade 11 lesson comparing a linear and an exponential lead service line replacement plan, with logarithms used to find when each plan reaches its target.
Grade 12 Lesson plan
A grade 12 math lesson where students build linear and exponential population models from two data points, project water demand, and test it against a plant's capacity.
Grade 10 Lesson plan
A grade 10 lesson comparing linear phosphorus loading to exponential algae-coverage growth in a fictional pond, using explicit formulas to distinguish the two models.
Grade 9 Lesson plan
A grade 9 lesson comparing a reservoir's constant-rate leak loss to a warm cove's percent-based algae growth, distinguishing linear from exponential models.
Grade 10 Worksheet
Grade 10 students test a constant-loss model against a halving model of chlorine residual, using sample readings from a fictional town's pressure zone.
Grade 12 Worksheet
A grade 12 worksheet in which students build and use an exponential decay function for chlorine residual across a fictional town distribution system.
Grade 11 Math problem set
A grade 11 problem set contrasting linear and exponential decay of a fictional tank's chlorine residual, building a half-life model and comparing summer and winter.
Grade 11 Math problem set
A grade 11 problem set contrasting a fixed-percent water rate increase with a steady pipe leak, using function models and average rate of change.
Grade 11 Math problem set
A grade 11 problem set comparing a fixed-step pay schedule with a percent-raise schedule at two fictional utilities, then pricing a license certification.
Grade 9 Math problem set
A grade 9 math problem set modeling a fictional lake's algal bloom, contrasting exponential growth before treatment with linear decline after treatment starts.
Grade 10 Lab / experiment
Students cool bottles of warm water four ways, from still air to an ice-water tub, calculate cooling rates, and advise a fictional school on heat stroke first aid.
Grade 11 Lab / experiment
Groups dry wet cloths in a fan draft, in still air, and under cover, then model drying with ratios and logarithms to explain why hidden wet materials grow mold.
Grade 11 Classroom activity
A 55-minute grade 11 station rotation where teams test four dam data sets with differences and ratios, then name and write the model family each one follows.
Grade 11 Quiz & test questions
A grade 11 quiz mixing multiple-choice, short-answer, and computation items on a fictional district's per-capita use, affordability, and rate growth.